3D Primary Geochemical HaloModeling and Its Application to the Ore Prediction of the Jiama Polymetallic Deposit, Tibet, China

The identification of primary geochemical haloes can be used to predict mineral resources in deep-seated orebodies through the delineation of element distributions. The Jiama deposits a typical skarn–porphyry Cu–polymetallic deposit in the Gangdese metallogenic belt of Tibet. The Cu–polymetallic skarn, Cu–Mo hornfels, and Mo±Cu porphyry mineralization there exhibit superimposed geochemical haloes at depth. Three-dimensional (3D) primary geochemical halo modeling was undertaken for the deposit with the aim of providing geochemical data to describe element distributions in 3D space. An overall geochemical zonation of Zn(Pb)→Au→Cu(Ag)→Mo gained from geochemical cross-sections, together with dipdirection skarn zonation Pb–Zn(Cu)→Cu(Au–Ag–Mo)→Mo(Cu)→Cu–Mo(Au–Ag) and vertical zonation Cu–(Pb– Zn)→Mo–(Cu)→Mo–Cu–(Ag–Au–Pb–Zn)→Mo in the #24 exploration profile, indicates potential mineralization at depth. Integrated geochemical anomalies were extracted by kernel principal component analysis, which has the advantage of accommodating nonlinear data. A maximum-entropy model was constructed for deep mineral resources of uncertainty prediction. Three potential deep mineral targets are proposed on the basis of the obtained geochemical information and background.


Introduction
Primary geochemical halo identification is a key approach for detecting mineral deposits near or below the ground surface [1]. A primary geochemical halo is an area of rocks surrounding mineral deposits (orebodies) enriched in ore-forming elements [2]. Primary geochemical characteristics of mineral deposits provide important information for predicting deep mineral resources, as they reflect the geochemical processes of metal precipitation and mineral formation. Many methods have been used to identify primary halo characteristics of mineral deposits, including vertical element zonation [3][4][5], element ratios vectoring toward ore zones [6][7][8], Pearce element ratios [1,[9][10][11][12], and alteration indices [13][14][15][16][17][18][19][20][21]. A major aspect of these methods is the determination of spatial distributions of single elements and/or element associations.
Within the Jiama Cu-polymetallic deposit in Tibet, previous studies focused on element zonation based on lithogeochemical data for surface samples and those from orebodies to build an exploration model for deep mineral resources [22][23][24][25][26][27][28][29]. Primary geochemical zonation and elemental distributions have thus been proved to be valid methods for estimating mineral resources at Jiama. Three-dimensional (3D) modeling is also an efficient approach that has been widely applied in deep mineral exploration [30][31][32][33], with 3D visualizations of primary geochemical haloes directly reflecting the spatial distribution of elements [34,35]. A 3D model of primary haloes can be useful in geochemical studies of mineral deposits because it provides insights into mineralization systems, with important implications for exploration. In this study, 3D halo modeling was undertaken to extend geochemical zonation to stereoscopic space to provide more information on deep mineral resources.
Lithogeochemical data from sources such as drill cores usually have nonlinear features that require processing by nonlinear algorithms. Kernel principal component analysis (KPCA) has been identified as a useful method for extracting integrated information from multielement drill-core data [36,37]. KPCA is a type of nonlinear PCA developed by extension of the kernel method [38] and involves the transfer of original inputs to a high-dimensional feature space by the kernel method with PCA of that space [39]. KPCA has been used in remote-sensing image classification [36,37], multidimensional space uncertainty modeling [40], anomaly detection in hyperspectral imagery [41], and volcanic reservoir fracture discrimination [42].
Machine learning (ML) has provided a new means of building models based on large data volumes [43][44][45]. ML algorithms that consider relationships between prediction and response variables through direct modeling have proved effective in capturing complex nonlinear relationships between geochemical models and mineralization [44,46], including the use of logic regression [43], neural networks [47], support vector machine [45], random forest [48], and maximum-entropy (MaxEnt) model [49,50]. A MaxEnt model is a high-performance statistical model often used in probabilistic estimation. It is suitable for classification problems and shows a performance superior to that of other methods, especially with limited sample data [51,52]. Max-Ent modeling has been widely applied in such fields as natural language processing [53,54], economic prediction [55], the geographical distribution of animal and plant species [56], and mineral resource prediction [49,50].
In this study, lithogeochemical data from drill cores were used to build a 3D primary geochemical halo model through spatial interpolation, aiming to describe element distributions at depth in the Jiama deposit. The cutting of crosssections and vertical profiles was applied to investigate spatial variations in different elements, and the KPCA method was used to produce profile integrated geochemical information, with MaxEnt modeling being applied to predict exploration targets.
Geological structures at Jiama are controlled by collision of the India and Eurasia plates and constitute E-trending strike-slip faults and related secondary NW-trending thrusts, including a major thrust nappe structure associated with a series of overturned folds and a gliding nappe covering 4 km 2 . These structures contributed to the formation of the Jiama Cu-polymetallic system [23,63,66].
Thermal and hydrothermal alteration has occurred in the Jiama deposit, with the former generating hornfels and marble [67] and the latter being related to porphyry and skarn alteration. Porphyry alteration (with porphyry as the center) changed from the proximal potassic zone (hydrothermal biotite + quartz + K-feldspar) to the middle phyllic zone (quartz + sericite + phengite) and then the peripheral propylitic zone (chlorite + epidote + calcite + quartz). Skarn alteration includes endoskarn and exoskarn, with the former occurring mainly as epidote alteration and the latter including garnet-pyroxene and wollastonite skarn [22,23,28,63].
On the basis of its different host rocks, the Jiama orebody can be divided into Cu-polymetallic skarn (orebodiesI and II), Cu-Mo hornfels (orebody III), and Mo ± Cu porphyry mineralization (orebody IV) [23]. Skarn orebody is regard as the most important orebody type at present as it constitutes over 70% of the reserves. In addition, porphyry orebody has raised much attention for its high mineral prospectivity [22,28,35,57]. 2.3. KPCA. KPCA was originally developed by Scholkopf et al. [38] and is aimed at converting original nonlinear inputs into a high-dimensional feature space through the kernel method, with PCA applied to this space [39]. Details of the fundamental theory of the method have been given by Scholkopf et al. [38,68]. Extraction of geochemical integrated information by KPCA follows the steps given below.

Geofluids
The lithogeochemical sample-data input dataset can be described as matrix A mn comprising n elements and m samples: (1) The Gaussian kernel (a classic kernel; [69]) is used to calculate the kernel matrix,K: (2) Eigenvalues λ 1 , ⋯, λ n of the kernel matrix and corresponding eigenvectors,ν 1 , ⋯, ν n , are calculated 3 Geofluids where L is the eigenvalue matrix and Y is the integrated geochemical information extraction by KPCA

MaxEnt
Model. The concept of information entropy was first introduced by Shannon [70] and represents the expected value of information contained in messages [71]. As a measure of the uncertainty of random events, the information entropy can be expressed as where HðpÞ represents the information entropy and p i is the probability of the ith random event. The probability distribution that best represents the current state of knowledge has the highest entropy, based on the MaxEnt principle [72]. The MaxEnt model is constructed according to this principle, together with a log-linear ML-based model. This model can set constraints flexibly and has been successfully applied in mineral resource prediction [49,50].     Figure 2 and Table 1).

3D Primary Geochemical
Sequences of primary haloes indicate elemental zonation in the deposit, as determined by comparison of elemental distributions.
The data presented in Figure 3 and Table 1 indicate a systematic vertical zonation pattern of Zn(Pb) → Au → -Cu(Ag) → Mo from surface to depth in the Jiama deposit. This zonation pattern also indicates two distinct parts of the deposit either side of~4650 m elevation, with Pb and Zn concentrated above and Au, Ag, Cu, and Mo below. This is consistent with the observed spatial distribution of different types of mineralization (Figure 4).

Mineral Prediction at Depth
3.2.1. Elemental Distributions in the Profile. The interpolation of values within 3D space provides a more reasonable value than interpolating over a profile. Furthermore, a profile of interest can be cut to investigate the distribution of elements in a certain region. Here, the #24 exploration profile is considered as an example, with a vertical data profile being cut to study elemental distributions.
The #24 exploration profile is typical one of the Jiama deposit as it contains all the orebody types, with hornfels mineralization in its upper part (4300-5200 m elevation); porphyry mineralization below 5000 m elevation as a cone shape amid the hornfels orebody; and skarn mineralization at the contact between porphyry and marble, and in the interlayer detachment zone between Linbuzong Formation hornfels and Duodigou Formation marble. The skarn orebody occurs in lamellar form or as thick plates and is found mainly at elevations of 4000-5000 m [23,24] (Figure 4).
A total of 7423 pieces of data were obtained from the profile cutting, with results indicating typical nonlinear features with high skewness, kurtosis, and coefficients of variation ( Table 2).
In the #24 exploration profile, hornfels and porphyry mineralization occur at elevations of >~4700 m, spatially consistent with the upper orebodies III and IV, respectively. Skarn mineralization at 4200-4700 m corresponds to orebody I. Molybdenite mineralization below 4700 m includes skarn, hornfels, and porphyry mineralization, which are related to orebodiesI, III, and IV, respectively. Lead and Zn mineralization occurs within Cu mineralization, mainly in the upper skarn orebody I. Au and Ag are hosted mainly within Cu mineralization as by-products of Cu extraction in the skarn orebody I [22][23][24][27][28][29] (Figures 4 and 5).
The geochemical profiles of Cu, Mo, Pb, Zn, Au, and Ag are shown in Figure 5. In skarn, the Cu grade is generally >1% and the Mo grade 0.08%-0.15%, compared with 0.15%-0.4% and~0.05%, respectively, in porphyry. There is  7 Geofluids a much higher mineralization intensity in skarn, which causes the Cu and Mo anomalies to be concealed in porphyry. Especially, the left part below skarn orebody I has high-grade Cu-Zn-Au-Ag mineralization, in which the drill holes in the #24 exploration profile did not reach. This anomaly is deduced from 3D interpolation, using data from the drill holes next to #24 exploration profiles. In such circumstances, geochemical zonation may be helpful in metal mineralization studies.
In skarn Cu-polymetallic orebody I, Pb and Zn are concentrated mainly in the upper left of the profile, Au and Ag along the orebody dip direction, and Mo in the distal part of dip direction ( Figure 5). The Cu content is lower where skarn orebody I and porphyry orebody IV intersect. The sequence Pb-Zn(Cu) → Cu(Au-Ag-Mo) → Mo(Cu) → Cu-Mo(Au-Ag) thus applies to the skarn orebody ( Figure 5).
Hornfels and porphyry orebodies III and IV clearly discriminate the upper Cu and lower Mo at an elevation of

Geofluids
~4750 m, consistent with the trends in Cu and Mo mineralization. Overall, the geochemical map and linear metal productivities in the #24 profile (Table 3) indicate elemental zonation of Cu(Pb-Zn) → Mo(Cu) → Mo-Cu(Ag-Au-Pb-Zn) → Mo from top to bottom. Linear productivity reflects the geochemical anomaly at a particular elevation and was calculated using where P is linear productivity, C ai is the value of the geochemical anomaly at aparticular location, d i is the length where C ai occurs (20 m here), C b is the value of the geochemical background, and n is the number of samples at the corresponding elevation.

Integrated Distribution in the #24 Exploration Profile.
Taking into account the nonlinear characteristics of the primary geochemical halo data (Table 2), the KPCA method was used to extract integrated multielement information for the #24 profile, with principal component 1 explaining 43.46% of the total variance of the kernel-transformed data ( Figure 6). Figure 6 highlights the two parts of the #24 profile, one with the upper of hornfels orebody above~4700 m and the other around the skarn orebody. The upper unit is characterized by Cu mineralization in hornfels above 4700 m, and the lower unit is associated with Cu-polymetallic mineralization in skarn.

Deep Mineral Resource Prediction for the #24 Profile.
The zonation of 3D primary geochemical haloes obtained from cross-section cutting (Section 3.1.2), Zn(Pb) → Au → -Cu(Ag) → Mo, is typical of elemental zonation in porphyry Cu mineralization systems, consistent with earlier findings [35,74], and may be useful for predicting element distributions at greater depth.
The zonation along the skarn orebody reflects Pb-Zn(Cu) → Cu(Au-Ag-Mo) → Mo(Cu) → Cu-Mo(Au-Ag) from upper left to bottom ( Figure 5), consistent with the distribution of associated elements around the porphyry intrusions. The skarn orebody I formed in the interlayer detachment zone between the Linbuzong and Duodigou formations and is confined to the contact between porphyry and marble. It dips NE and is~3000 m long, with a tendency to extended mineralization [23,24] (Figures 4-6). Moreover, the zonation along the skarn orebody is incomplete and should include an association of Cu-Au-Ag or Cu-Pb-Zn, indicating potential Cu-polymetallic mineralization.
The zonation of element associations from top to bottom of the #24 exploration profile, Cu(Pb-Zn) → Mo(Cu) → Mo-Cu(Ag-Au-Pb-Zn) → Mo, is affected by the different mineralization types. The Cu(Pb-Zn) association is derived from the skarn orebody at an elevation of~4750 m, the Mo(Cu) association involves the hornfels orebody at~4650 m, the Mo-Cu(Ag-Au-Pb-Zn) association reflects the composition of the skarn orebody at~4400 m, and the Mo anomaly at the bottom may indicate deep porphyry molybdenite mineraliza-tion. This is especially the case for the profile across the center of the porphyry and hornfels orebodies, where zonation may be an important indicator of deep mineral resources.
The MaxEnt model was applied to the analysis of uncertainties in mineral resource prediction based on elemental distribution ( Figure 5), integrated anomalies ( Figure 6), and the locations of orebodies. The MaxEnt software was used to establish a prediction model for prospective mineral resource areas (MaxEnt 3.3.3k; http:// biodiversityinformatics.amnh.org/open_source/maxent/), with model parameters as given in Table 4. In this simulation, 75% of the data were randomly selected as ML training data and the remaining 25% as test data. The MaxEnt software performed 20 replicated simulations on the optimal model to provide the average value of the model evaluation with the test AUC ðArea Under CurveÞ = 0:929 (Figure 7), which indicates that the model was able to successfully associate the probability of multivariate geochemical anomalies with mineralizations. As shown in Figure 8, mineralizations in #24 profile are spatially consistent with the high anomaly probability zone (red), which could be used as evidence in predicting the location of concealed orebodies with consideration of uncertainty.

Discussion
Target 24-1 lies below borehole ZK2409 at an elevation of 4250 m and is indicated by both multielement anomalies and an integrated KPCA anomaly (Table 1; Figures 5 and  6). The MaxEnt model indicates that this target has a high probability of containing mineral resources and warrants further investigation, as it may be related to a deep porphyry edge or second concealed skarn layer (Figure 8).
Target 24-2 lies under porphyry orebody IV, where a high-Mo anomaly is evident with increasing Mo concentration with depth ( Figure 5 and Table 1). The geochemical zonation from top to bottom of the #24 exploration profile, Cu(Pb-Zn) → Mo(Cu) → Mo-Cu(Ag-Au-Pb-Zn) → Mo, provides strong support for this target. From a geological perspective, the extensive deep porphyry suggests a significant prediction direction for as-yet-unidentified porphyry Mo(Cu) mineralizations. A high probability of mineralization that shows in Figure 8 provides the reference of mineral location.    10 Geofluids providing a strong support for the targets above. The MaxEnt model can evaluate the uncertainty of the predicted targets of 24-1 and 24-2, which is also a quantitative evidence for mineralization ( Figure 8).

Conclusions
(1) In this study, 3D primary geochemical halo modeling was used to build a geochemical data volume by 3D spatial interpolation. In this approach, information was obtained from all directions in 3D space, which is an improvement over interpolation on a fixed surface (3) During the analysis process, an integrated geochemical map was generated by KPCA, and a MaxEnt model was built by combining six single-element geochemical anomalies and an integrated geochemical anomaly for deep mineral resource uncertainty prediction. Finally, three deep-seated mineral targets were identified by the geological and geochemical information extracted from the 3D primary geochemical halo modeling

Data Availability
The data used to support the findings of this study were supplied by Huatailong mining industry development Co., Ltd. and so cannot be made freely available. Requests for access to these data should be made to Huatailong mining industry development Co., Ltd.

Conflicts of Interest
The authors declare no conflicts of interest.
Authors' Contributions Z.T., B.L., and K.G. contributed to the ideas. B.L. and Z.T contributed to the methodology. Z.T., B.L., C.L., Y.X., and Y.L. contributed to the writing for the original draft preparation. B.L. contributed to the writing involving review and editing. N.G. and C.L. contributed to the modeling. K.G. con-tributed to the supervision. All authors read and agreed to the published version of the manuscript.